Relative and absolute error calculator
Calculator finds out absolute or relative error basing it on measured (calculated) and reference (ideal) value.

# Beta version#

BETA TEST VERSION OF THIS ITEM
This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
Feel free to send any ideas and comments !

# Symbolic algebra

ⓘ Hint: This calculator supports symbolic math. You can enter numbers, but also symbols like a, b, pi or even whole math expressions such as (a+b)/2. If you still don't sure how to make your life easier using symbolic algebra check out our another page: Symbolic calculations

# What do you want to calculate today?#

 Choose a scenario that best fits your needs I know measured value (x) and reference values ($x_0$) and want to calculate absolute error ($\Delta x$)I know measured value (x) and reference values ($x_0$) and want to calculate relative error ($\delta x_{rel.}$)

# Calculations data - enter values, that you know here#

 Absolute error ($\Delta x$) => Relative error ($\delta x_{rel.}$) => Measured value (x) <= Reference values ($x_0$) <=

# Result: absolute error ($\Delta x$)#

Summary
Used formulaShow source$\Delta x=\left|x-x_0\right|$
ResultShow source$\frac{39816339744831}{25000000000000000}$
Numerical resultShow source$0.00159265358979324$
Result step by step
 1 Show source$\left|3.14-3.14159265358979324\right|$ Convert decimal to fraction Decimal number can be converted into fraction with denominator 10, 100, 1000 etc. 2 Show source$\left|\frac{157}{50}-3.14159265358979324\right|$ Convert decimal to fraction Decimal number can be converted into fraction with denominator 10, 100, 1000 etc. 3 Show source$\left|\frac{157}{50}-\frac{78539816339744831}{25000000000000000}\right|$ Common denominator Before add two fractions, we need convert them into common denominator. We can find the optimal common denominator using the lowest common multiply (LCM) from both denominators. 4 Show source$\left|\frac{157 \cdot 500000000000000-78539816339744831}{25000000000000000}\right|$ Simplify arithmetic - 5 Show source$\left|\frac{78500000000000000-78539816339744831}{25000000000000000}\right|$ Simplify arithmetic - 6 Show source$\left|\frac{-39816339744831}{25000000000000000}\right|$ Absolute value |c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right. 7 Show source$\frac{\left|-39816339744831\right|}{\left|25000000000000000\right|}$ Absolute value |c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right. 8 Show source$\frac{39816339744831}{\left|25000000000000000\right|}$ Absolute value |c| = \left \{ \begin{aligned} &c && \text{, if}\ c \ge 0 \\ &-c && \text{, if}\ c \lt 0 \end{aligned} \right. 9 Show source$\frac{39816339744831}{25000000000000000}$ Result Your expression reduced to the simplest form known to us.
Numerical result step by step
 1 Show source$0.00159265358979324$ The original expression - 2 Show source$0.00159265358979324$ Result Your expression reduced to the simplest form known to us.

# Some facts#

• Absolute error is the absolute value of the difference between measured value (calculated, approximate etc.) and reference value (ideal, theoretical etc.):
$\Delta x = |x-x_0|$
where:
• $\Delta x$ - absolute error,
• $x$ - measured, calculated or approximate value of variable $x$,
• $x_0$ - the reference value against which we calculate the error.
• Relative error determines the size of the error made presented as part of the reference value:
$\delta x_{wzgl.} = \left|\dfrac{x-x_0}{x_0}\right|$
where:
• $\delta x_{rel.}$ - error expressed as a part of the reference value,
• $x$ - measured, calculated or approximate value of variable $x$,
• $x_0$ - the reference value against which we calculate the error.
• When we determine the error, we are generally not trying to find out whether the value obtained is too large or too small, but only how big the error is. This is the reason why error formula has the absolute value form.
• In the case of values with units (e.g. length measured in meters), the absolute error has the same units as the measured one. For example, an absolute error of length value is also the length.
• Relative error has no units, no metter what do we measure. Relative error is often presented as percent.

# Tags and links to this website#

Tags:
Tags to Polish version: